Find the mean and variance for the data $6, 7, 10, 12, 13, 4, 8, 12$.

In a distribution of $10$ observations,the sum of the observations is $60$ and the sum of their squares is $1000$. Then,the variance is:

The variance of the following frequency distribution is:

Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$11$	$29$	$18$	$4$	$5$	$3$

Statement $1$: The variance of the first $n$ odd natural numbers is $\frac{n^2 - 1}{3}$.
Statement $2$: The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n(4n^2 - 1)}{3}$.

The arithmetic mean of marks in Mathematics for four divisions $A, B, C$ and $D$ were $80, 75, 70$ and $72$ respectively. Their standard deviations were $12, 6, 8$ and $10$ respectively. Then,which division has more uniformity?

Find the mean and variance for the following frequency distribution:

Classes	$0-30$	$30-60$	$60-90$	$90-120$	$120-150$	$150-180$	$180-210$
$f_i$	$2$	$3$	$5$	$10$	$3$	$5$	$2$